3rd French conference on acoustics
J. Phys. IV France 04 (1994) C5-685-C5-688
Interprétation physique des ondes de Floquet se propageant dans un milieu multicouche périodique anisotropeC. POTEL and J.-F. DE BELLEVAL
Université de Technologie de Compiègne, Centre de Recherches de Royallieu, LG2mS, URA 1505 du CNRS, BP. 649, 60206 Compiègne cedex, France
The aim of this paper is to better understand the correspondence between the classical plane waves propagating in each layer of an anisotropic periodically multilayered medium and the Floquet waves. The last are linear combinations of the classical plane waves. Their wave number is obtained from the eigenvalues of the transfer matrix of one cell of the medium. We have defined a Floquet polarisation which varies with its position in the periodically multilayered medium. This allows us to define a Floquet waves displacement by analogy with the one of the classical plan waves, and to verify the equality of the two displacements at any interface separating two layers. The periodically multilayered medium is then equivalent to a dummy material, and one can draw dispersion curves. In low frequencies range, when the relation between the Floquet wave numbers and the frequency is linear, the multilayered medium can be homogenised ; the Floquet polarisation at different interfaces tends to a limit which is the polarisation of the classical plane wave in the homogenised medium.
© EDP Sciences 1994